David Cameron came under fresh pressure to reveal whether he sought Cabinet Office approval prior to meeting James Murdoch and Rebekah Brooks at Christmas in the midst of the News Corp bid for BSkyB.

No 10 is due to reply on Tuesday to written questions asking Cameron whether he sought civil service advice on the wisdom of going ahead with the meeting at such a sensitive time.

The pressure came as No 10 disclosed a further meeting between Brooks and Cameron at his birthday party.

Downing Street on Friday gave what was intended to be a complete list of Cameron's meetings with senior newspaper executives and whether they were social or business related. The list revealed that Cameron had met Brooks, News International chief executive, four times since he became prime minister. No 10 said the birthday party was not on the list because it had only just been recalled that she was present.

The list showed 26 meetings or events involving News International figures, nine involving Telegraph Media Group, four for Associated Newspapers, publisher of the Daily Mail and Mail on Sunday; and four involving the Evening Standard.

Government ministers are due to list their parallel engagements with newspaper executives in the next few days.

Ivan Lewis, the shadow culture secretary, has been pressing Cameron for months to give details of the meetings between Brooks and Cameron, to be told the decision on the takeover was a matter for the culture secretary, Jeremy Hunt, alone. Cameron has not said whether he discussed the issue with Hunt at any point.

Cameron met Brooks for dinner at her Chipping Norton home on 23 December, and the following day had a family picnic with the Brooks family. The picnic was disclosed by the motoring correspondent Jeremy Clarkson in his Sunday Times column. He insists the discussion at dinner contained no mention of any political or business matter.

Lewis said: "David Cameron's promise of greater transparency over meetings with media executives will ring hollow unless he comes clean about the nature of the discussions which took place at his dinner with Rebekah Brooks last Christmas. His judgment is in serious question, and so is the nature of the conversations he had with his friend Rebekah Brooks.

"The dinner came just days after he handed responsibility for the BSkyB deal from Vince Cable to Jeremy Hunt. Did he discuss this with Rebekah Brooks over dinner?"

So far Cameron has only given one partial answer, writing to Lewis on 17 February: "I have no role in the process. This is a decision for the culture secretary in a quasi-judicial role based on available evidence. It is a decision for him alone. Therefore the first I heard about the decision was when it was announced."

Lewis has again written to Cameron to ask whether he received any advice from the cabinet secretary as to whether his meeting with Brooks was in line with the ministerial code.

Cameron also came under pressure from Labour MPs for failing to apologise for appointing Andy Coulson as his communications director. Labour sought to contrast the way two senior policemen, Sir Paul Stephenson and John Yates, resigned over the appointment of the former News of the World deputy editor Neil Wallis, and Cameron's refusal to apologise for appointing the paper's former editor Coulson.

Ed Miliband, the Labour leader, said: "It is also striking that Sir Paul Stephenson has taken responsibility and resigned over the employment of Mr Coulson's deputy, while the prime minister hasn't even apologised for hiring Mr Coulson. We need leadership to get to the truth of what happened. But David Cameron is hamstrung by his own decisions and his unwillingness to face up to them."

Theresa May, the home secretary, insisted there was no comparison between the appointments of Wallis and Coulson. She said: "There is a very real difference between the Met and the government. The Met are responsible for looking at alleged wrongdoing by the News of the World. It is important there is a line between the investigators and the investigated."

Cameron spoke to Stephenson on Monday in an attempt to calm relations between the two.